A parabola can be drawn given a focus of (7,−10) and a directrix of y=10. What can be said about the parabola?

Options B and E are correct.

Step-by-step explanation:

Let the equation of the given line is y = mx + c

This line passes through two points (1, 13) and (-2, 4)

So slope of the line m =

m =

y-intercept of the line is 10

Therefore equation will be y = 3x + 10

Now we take the options one by one.

A. y - 2 = 3(x - 4)

y = 2 + 3x - 12

y = 3x - 10

Option is incorrect because the given line in this option doesn't matches with the equation of the line.

B. y - 4 = 3(x + 2)

y = 4 + 3x + 6

y = 3x + 10

Correct option.

C. y - 1 = 3(x - 13)

y = 1 + 3x - 39

y = 3x - 38

Incorrect option.

D. y - 4 = 3( x- 2 )

y = 4 + 3x - 6

y = 3x - 2

Incorrect option

E. y - 13 = 3(x - 1)

y = 13 + 3x -3

y = 3x + 10

Correct option.

F. y + 2 = 3(x - 4)

y = -2 + 3x - 12

y = 3x - 14

Incorrect option.

Therefore, Options B and E are the correct options.